Why is it better to anchor under the chin than just below the eye?

The arrow trajectory is almost the same wherever the anchor is located.  However, the sight is always lined up on or near the centre of the target.  At long ranges the bow has to be raised to get the necessary flight path and this leaves the sight behind.  If the nock end of the arrow is just under the eye then the point can easily be raised high enough that there is interference between the arrow and the sight.  It is possible to position the sight below the arrow to avoid this interference but then the arrow is likely to obscure the sight (see note on maximising the range). By anchoring under the chin the bow can be elevated to a greater angle before interference occurs.  A further advantage of his position is the more precise anchor that is possible with the lower jaw in contact with the index finger or platform of an anchor tab.

More extreme methods have been used to increase the distance between the eye and the nock.  These include putting some object between the teeth (to give a stable reference as well as increasing the distance) and using a kisser placed so that the upper teeth are used as the reference while an open mouth gives feel to the shot.